code: def test_lerchphi_expansion():
      assert myexpand(lerchphi(1, s, a), zeta(s, a))
      assert myexpand(lerchphi(z, s, 1), polylog(s, z) / z)
  
      # direct summation
      assert myexpand(
          lerchphi(z, -1, a), a / (1 - z) + z / (1 - z) ** 2
      )
      assert myexpand(lerchphi(z, -3, a), None)
      # polylog reduction
      assert myexpand(
          lerchphi(z, s, S.Half),
          2 ** (s - 1)
          * (
              polylog(s, sqrt(z)) / sqrt(z)
              - polylog(s, polar_lift(-1) * sqrt(z)) / sqrt(z)
          ),
      )
      assert myexpand(
          lerchphi(z, s, 2), -1 / z + polylog(s, z) / z**2
      )
      assert myexpand(lerchphi(z, s, Rational(3, 2)), None)
      assert myexpand(lerchphi(z, s, Rational(7, 3)), None)
      assert myexpand(lerchphi(z, s, Rational(-1, 3)), None)
      assert myexpand(lerchphi(z, s, Rational(-5, 2)), None)
  
      # hurwitz zeta reduction
      assert myexpand(
          lerchphi(-1, s, a),
          2 ** (-s) * zeta(s, a / 2) - 2 ** (-s) * zeta(s, (a + 1) / 2),
      )
      assert myexpand(lerchphi(I, s, a), None)
      assert myexpand(lerchphi(-I, s, a), None)
      assert myexpand(
          lerchphi(exp(I * pi * Rational(2, 5)), s, a), None
      )
  
imports: from sympy.concrete.summations import Sum
  from sympy.core.function import expand_func
  from sympy.core.numbers import Float, I, Rational, nan, oo, pi, zoo
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.elementary.complexes import Abs, polar_lift
  from sympy.functions.elementary.exponential import exp, exp_polar, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.special.zeta_functions import dirichlet_eta, lerchphi, polylog, riemann_xi, stieltjes, zeta
  from sympy.series.order import O
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic
  from sympy.testing.pytest import raises
  from sympy.core.random import test_derivative_numerically, random_complex_number, verify_numerically
label_desc: Use image node_id 12 for calling a global function with example usage: test_lerchphi_expansion() without return types